https://mklab.gr/ Sun, 18 Oct 2026 03:19:49 +0000 MyBB https://mklab.gr/showthread.php?tid=2176 Fri, 25 Sep 2026 18:54:03 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=2176 Optimization: A Bootcamp for Machine Learning, Inverse Problems, and Control by Steven L. Brunton is a 2026 Cambridge University Press textbook that presents optimization as a central mathematical tool connecting modern engineering, machine learning, inverse problems, and control. The book is designed as a “bootcamp”: it starts from relatively accessible material, assuming mainly basic linear algebra and calculus, and progressively develops more sophisticated optimization techniques. At 509 pages, it is intended for advanced undergraduates, beginning graduate students, and practitioners in science and engineering.

The central theme is that optimization provides a common language for problems that at first appear unrelated. In machine learning, optimization is used to fit models and minimize loss functions; in inverse problems, it helps infer unknown parameters, structures, or causes from observed data; and in control, it provides a systematic way to choose inputs that make a dynamical system behave as desired. The book therefore emphasizes the mathematical structure underlying these applications rather than treating optimization merely as a collection of algorithms.

Brunton combines mathematical explanation with computational experimentation. The book includes Python code, simple working examples, and more advanced case studies, allowing readers to move between equations, algorithms, and practical applications. Online material also includes video lectures, with the stated goal of making the subject interactive and accessible while retaining sufficient mathematical depth for research and real-world work. This combination is particularly useful for learners who need to understand not only how an optimization algorithm works, but also why a particular formulation is appropriate for a problem.

Overall, the book can be viewed as a bridge between classical applied mathematics and modern AI/data-driven science. Rather than isolating optimization as a traditional numerical-analysis topic, it shows how ideas such as least squares, regularization, constrained optimization, and related computational methods feed directly into contemporary machine learning, system identification, inverse modeling, and optimal control. For a mathematics teacher interested in connecting university-level mathematics with AI, it offers a particularly relevant framework because optimization becomes the mathematical thread linking calculus, linear algebra, computation, data, and dynamical systems.

Key takeaways

• Optimization is a foundational mathematical language for modern engineering, technology, and AI.
  
• The book connects three major application areas: machine learning, inverse problems, and control.
  
• It assumes mainly basic calculus and linear algebra, making it suitable as an entry point to applied optimization.
  
• The progression is from an introductory “Optimization Bootcamp” toward advanced and research-oriented methods.
  
• Python examples connect mathematical theory with actual computation.
  
• Inverse problems illustrate how optimization can recover unknown quantities from incomplete or indirect observations.
  
• Control problems show optimization being applied to dynamical systems and decision-making.
  
• The book emphasizes the connection between mathematical formulation, algorithms, and applications, rather than algorithms in isolation.
  
• It is suitable for advanced undergraduates, beginning graduate students, and scientists/engineers.
  
• For mathematics education, it provides a useful pathway from calculus + linear algebra → optimization → machine learning and AI.
  

BOOK]]> Optimization: A Bootcamp for Machine Learning, Inverse Problems, and Control by Steven L. Brunton is a 2026 Cambridge University Press textbook that presents optimization as a central mathematical tool connecting modern engineering, machine learning, inverse problems, and control. The book is designed as a “bootcamp”: it starts from relatively accessible material, assuming mainly basic linear algebra and calculus, and progressively develops more sophisticated optimization techniques. At 509 pages, it is intended for advanced undergraduates, beginning graduate students, and practitioners in science and engineering.

The central theme is that optimization provides a common language for problems that at first appear unrelated. In machine learning, optimization is used to fit models and minimize loss functions; in inverse problems, it helps infer unknown parameters, structures, or causes from observed data; and in control, it provides a systematic way to choose inputs that make a dynamical system behave as desired. The book therefore emphasizes the mathematical structure underlying these applications rather than treating optimization merely as a collection of algorithms.

Brunton combines mathematical explanation with computational experimentation. The book includes Python code, simple working examples, and more advanced case studies, allowing readers to move between equations, algorithms, and practical applications. Online material also includes video lectures, with the stated goal of making the subject interactive and accessible while retaining sufficient mathematical depth for research and real-world work. This combination is particularly useful for learners who need to understand not only how an optimization algorithm works, but also why a particular formulation is appropriate for a problem.

Overall, the book can be viewed as a bridge between classical applied mathematics and modern AI/data-driven science. Rather than isolating optimization as a traditional numerical-analysis topic, it shows how ideas such as least squares, regularization, constrained optimization, and related computational methods feed directly into contemporary machine learning, system identification, inverse modeling, and optimal control. For a mathematics teacher interested in connecting university-level mathematics with AI, it offers a particularly relevant framework because optimization becomes the mathematical thread linking calculus, linear algebra, computation, data, and dynamical systems.

Key takeaways

• Optimization is a foundational mathematical language for modern engineering, technology, and AI.
  
• The book connects three major application areas: machine learning, inverse problems, and control.
  
• It assumes mainly basic calculus and linear algebra, making it suitable as an entry point to applied optimization.
  
• The progression is from an introductory “Optimization Bootcamp” toward advanced and research-oriented methods.
  
• Python examples connect mathematical theory with actual computation.
  
• Inverse problems illustrate how optimization can recover unknown quantities from incomplete or indirect observations.
  
• Control problems show optimization being applied to dynamical systems and decision-making.
  
• The book emphasizes the connection between mathematical formulation, algorithms, and applications, rather than algorithms in isolation.
  
• It is suitable for advanced undergraduates, beginning graduate students, and scientists/engineers.
  
• For mathematics education, it provides a useful pathway from calculus + linear algebra → optimization → machine learning and AI.
  

BOOK]]> https://mklab.gr/showthread.php?tid=2126 Wed, 23 Sep 2026 23:40:20 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=2126 Practical Optimization by Philip E. Gill, Walter Murray, and Margaret H. Wright is a comprehensive treatment of numerical optimization, originally published in 1981 and republished by SIAM in 2019. The book develops the mathematical foundations needed to formulate and solve optimization problems, beginning with objective functions, constraints, numerical errors, and optimality conditions. It then progresses through unconstrained optimization, problems with linear constraints, and more difficult nonlinear constraints, emphasizing both the mathematical reasoning behind algorithms and their computational implementation.

A major strength of the book is its practical algorithmic perspective: it provides step-by-step descriptions and pseudocode rather than treating optimization purely theoretically. The later chapters address mathematical modeling and the practical difficulties encountered when implementing optimization methods, including numerical issues and strategies for dealing with real-world problems. 

Although many developments in optimization have occurred since the original edition, SIAM notes that the fundamental principles and intuition remain relevant, including for modern applications in data science, large-scale computation, and machine learning,

BOOK]]> Practical Optimization by Philip E. Gill, Walter Murray, and Margaret H. Wright is a comprehensive treatment of numerical optimization, originally published in 1981 and republished by SIAM in 2019. The book develops the mathematical foundations needed to formulate and solve optimization problems, beginning with objective functions, constraints, numerical errors, and optimality conditions. It then progresses through unconstrained optimization, problems with linear constraints, and more difficult nonlinear constraints, emphasizing both the mathematical reasoning behind algorithms and their computational implementation.

A major strength of the book is its practical algorithmic perspective: it provides step-by-step descriptions and pseudocode rather than treating optimization purely theoretically. The later chapters address mathematical modeling and the practical difficulties encountered when implementing optimization methods, including numerical issues and strategies for dealing with real-world problems. 

Although many developments in optimization have occurred since the original edition, SIAM notes that the fundamental principles and intuition remain relevant, including for modern applications in data science, large-scale computation, and machine learning,

BOOK]]> https://mklab.gr/showthread.php?tid=2118 Wed, 23 Sep 2026 23:20:23 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=2118 The Basics of Practical Optimization, Second Edition by Adam B. Levy is an undergraduate-oriented introduction to optimization that emphasizes how optimization is actually used to solve practical problems, rather than treating it simply as an application of calculus. The book begins with mathematical modeling, explaining how real-world problems are translated into variables, objective functions, and constraints, and then develops derivative-based techniques such as Newton and quasi-Newton methods. It also discusses how to evaluate optimization algorithms in terms of computational effort, convergence, and the characteristics of the problem being solved.

A major strength of the book is its broad treatment of optimization beyond traditional calculus. It introduces constrained optimization, derivative-free methods, direct and random search, linear programming, integer programming, network optimization, and dynamic programming, with exercises, computational problems, implementations, and strategically placed Python notes. 

The overall approach is highly practical: readers learn not only mathematical theory but also how to formulate problems computationally and choose an appropriate method when derivatives are unavailable, constraints are important, or variables must be discrete. It is designed primarily for students who have completed multivariable calculus and can serve as an accessible introduction to modern applied optimization.

BOOK]]> The Basics of Practical Optimization, Second Edition by Adam B. Levy is an undergraduate-oriented introduction to optimization that emphasizes how optimization is actually used to solve practical problems, rather than treating it simply as an application of calculus. The book begins with mathematical modeling, explaining how real-world problems are translated into variables, objective functions, and constraints, and then develops derivative-based techniques such as Newton and quasi-Newton methods. It also discusses how to evaluate optimization algorithms in terms of computational effort, convergence, and the characteristics of the problem being solved.

A major strength of the book is its broad treatment of optimization beyond traditional calculus. It introduces constrained optimization, derivative-free methods, direct and random search, linear programming, integer programming, network optimization, and dynamic programming, with exercises, computational problems, implementations, and strategically placed Python notes. 

The overall approach is highly practical: readers learn not only mathematical theory but also how to formulate problems computationally and choose an appropriate method when derivatives are unavailable, constraints are important, or variables must be discrete. It is designed primarily for students who have completed multivariable calculus and can serve as an accessible introduction to modern applied optimization.

BOOK]]> https://mklab.gr/showthread.php?tid=2115 Wed, 23 Sep 2026 23:13:17 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=2115 An Introduction to Convexity, Optimization, and Algorithms by Heinz H. Bauschke and Walaa M. Moursi is a concise 2023 textbook that develops the mathematical foundations of convex analysis and optimization and then connects them directly to computational algorithms. It begins with affine and convex sets, convex and lower-semicontinuous functions, minimizers, support functions, projections, subgradients, normal cones, derivatives, and duality. The later chapters move toward optimality conditions such as the Karush–Kuhn–Tucker conditions, Fenchel–Rockafellar duality, and smoothness/Lipschitz continuity. 

The central theme is turning this theory into practical optimization methods. The book develops algorithms including the proximal-gradient method, FISTA (fast iterative soft-thresholding), Douglas–Rachford, and Peaceman–Rachford splitting, with Julia examples and more than 200 exercises. 

These methods are particularly relevant to modern computational mathematics, machine learning, signal processing, image reconstruction, and data science. Overall, the book serves as a bridge between rigorous mathematical convex analysis and the algorithms used to solve large-scale optimization problems.

BOOK]]> An Introduction to Convexity, Optimization, and Algorithms by Heinz H. Bauschke and Walaa M. Moursi is a concise 2023 textbook that develops the mathematical foundations of convex analysis and optimization and then connects them directly to computational algorithms. It begins with affine and convex sets, convex and lower-semicontinuous functions, minimizers, support functions, projections, subgradients, normal cones, derivatives, and duality. The later chapters move toward optimality conditions such as the Karush–Kuhn–Tucker conditions, Fenchel–Rockafellar duality, and smoothness/Lipschitz continuity. 

The central theme is turning this theory into practical optimization methods. The book develops algorithms including the proximal-gradient method, FISTA (fast iterative soft-thresholding), Douglas–Rachford, and Peaceman–Rachford splitting, with Julia examples and more than 200 exercises. 

These methods are particularly relevant to modern computational mathematics, machine learning, signal processing, image reconstruction, and data science. Overall, the book serves as a bridge between rigorous mathematical convex analysis and the algorithms used to solve large-scale optimization problems.

BOOK]]> https://mklab.gr/showthread.php?tid=2114 Wed, 23 Sep 2026 23:10:09 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=2114 Problems and Solutions for Integer and Combinatorial Optimization: Building Skills in Discrete Optimization by Mustafa Ç. Pınar and Deniz Akkaya is a 2023 SIAM book designed as a problem-solving resource for undergraduate and beginning graduate students in mathematics, computer science, and engineering. Rather than functioning primarily as a conventional textbook, it presents 102 problems of varying difficulty together with complete solutions, allowing readers to develop practical skills in discrete optimization. The material covers mathematical modeling with integer variables, graph and network problems, shortest paths, flows, trees, matching, and related optimization structures.

The book is organized into three major problem-solving areas. The first develops integer-variable modeling, including applications such as logical circuits; the second focuses on classical combinatorial optimization problems such as shortest paths, maximum flows, trees, and matching; and the third examines the deeper structure and solution of integer optimization problems, including integer points and convex-hull ideas. 

The solutions section then works through the problems in detail, making the book particularly useful for self-study, university courses, and building intuition about how discrete optimization problems are formulated and solved.

BOOK]]> Problems and Solutions for Integer and Combinatorial Optimization: Building Skills in Discrete Optimization by Mustafa Ç. Pınar and Deniz Akkaya is a 2023 SIAM book designed as a problem-solving resource for undergraduate and beginning graduate students in mathematics, computer science, and engineering. Rather than functioning primarily as a conventional textbook, it presents 102 problems of varying difficulty together with complete solutions, allowing readers to develop practical skills in discrete optimization. The material covers mathematical modeling with integer variables, graph and network problems, shortest paths, flows, trees, matching, and related optimization structures.

The book is organized into three major problem-solving areas. The first develops integer-variable modeling, including applications such as logical circuits; the second focuses on classical combinatorial optimization problems such as shortest paths, maximum flows, trees, and matching; and the third examines the deeper structure and solution of integer optimization problems, including integer points and convex-hull ideas. 

The solutions section then works through the problems in detail, making the book particularly useful for self-study, university courses, and building intuition about how discrete optimization problems are formulated and solved.

BOOK]]> https://mklab.gr/showthread.php?tid=2112 Wed, 23 Sep 2026 23:03:24 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=2112 Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with Python and MATLAB, Second Edition, by Amir Beck, is a graduate/advanced-undergraduate introduction to the mathematical foundations and computational methods of nonlinear optimization. The book develops the subject progressively, beginning with calculus, linear algebra, optimality conditions, and least-squares problems, then moving to gradient and Newton methods, convex sets and convex functions, and convex optimization. It emphasizes the connection between mathematical theory and practical algorithms rather than treating optimization purely analytically.

The later chapters focus on constrained optimization, including optimization over convex sets, linearly constrained problems, the Karush–Kuhn–Tucker (KKT) conditions, and duality. A distinctive feature of the second edition is its treatment of topics such as sparsity-constrained optimization, hidden convexity, and total least squares, together with applications including denoising, clustering, circle fitting, the Fermat–Weber problem, and orthogonal regression. 

Python and MATLAB implementations—including CVXPY and MATLAB's CVX toolbox—are used to connect the mathematics with actual computation, supported by more than 250 theoretical, algorithmic, and numerical exercises.

BOOK]]> Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with Python and MATLAB, Second Edition, by Amir Beck, is a graduate/advanced-undergraduate introduction to the mathematical foundations and computational methods of nonlinear optimization. The book develops the subject progressively, beginning with calculus, linear algebra, optimality conditions, and least-squares problems, then moving to gradient and Newton methods, convex sets and convex functions, and convex optimization. It emphasizes the connection between mathematical theory and practical algorithms rather than treating optimization purely analytically.

The later chapters focus on constrained optimization, including optimization over convex sets, linearly constrained problems, the Karush–Kuhn–Tucker (KKT) conditions, and duality. A distinctive feature of the second edition is its treatment of topics such as sparsity-constrained optimization, hidden convexity, and total least squares, together with applications including denoising, clustering, circle fitting, the Fermat–Weber problem, and orthogonal regression. 

Python and MATLAB implementations—including CVXPY and MATLAB's CVX toolbox—are used to connect the mathematics with actual computation, supported by more than 250 theoretical, algorithmic, and numerical exercises.

BOOK]]> https://mklab.gr/showthread.php?tid=2109 Wed, 23 Sep 2026 22:55:47 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=2109 A First Course in Linear Optimization by Amir Beck and Nili Guttmann-Beck is a 2025 SIAM textbook that develops the foundations of linear optimization from both theoretical and algorithmic perspectives. Starting with linear programming formulations and basic feasible solutions, it introduces the simplex method, duality, and sensitivity analysis, showing how mathematical theory translates into practical optimization procedures. The book also connects linear programming with applications including resource allocation, line fitting, graph coloring, network flows, the traveling salesman problem, and game theory. It is designed as a first undergraduate course and assumes only a first course in linear algebra. 

The second half expands from continuous linear programming to discrete and combinatorial optimization. It introduces integer programming, total unimodularity, Gomory cutting planes, and branch-and-bound, explaining why many integer problems are computationally difficult and how practical algorithms nevertheless solve important instances. 

Later chapters cover the maximum-flow problem, dynamic programming, and approximation algorithms, giving the reader a broader view of how optimization problems can be attacked when exact solutions are difficult. With 13 chapters and more than 180 exercises, the book aims to combine rigorous mathematical explanations with algorithms and applications rather than treating linear optimization purely as an abstract theory.

BOOK]]> A First Course in Linear Optimization by Amir Beck and Nili Guttmann-Beck is a 2025 SIAM textbook that develops the foundations of linear optimization from both theoretical and algorithmic perspectives. Starting with linear programming formulations and basic feasible solutions, it introduces the simplex method, duality, and sensitivity analysis, showing how mathematical theory translates into practical optimization procedures. The book also connects linear programming with applications including resource allocation, line fitting, graph coloring, network flows, the traveling salesman problem, and game theory. It is designed as a first undergraduate course and assumes only a first course in linear algebra. 

The second half expands from continuous linear programming to discrete and combinatorial optimization. It introduces integer programming, total unimodularity, Gomory cutting planes, and branch-and-bound, explaining why many integer problems are computationally difficult and how practical algorithms nevertheless solve important instances. 

Later chapters cover the maximum-flow problem, dynamic programming, and approximation algorithms, giving the reader a broader view of how optimization problems can be attacked when exact solutions are difficult. With 13 chapters and more than 180 exercises, the book aims to combine rigorous mathematical explanations with algorithms and applications rather than treating linear optimization purely as an abstract theory.

BOOK]]> https://mklab.gr/showthread.php?tid=1680 Mon, 17 Aug 2026 20:13:12 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1680 Integer Programming
Authors: Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli
Publication date: 2014
Publisher: Springer International Publishing
Series:Graduate Texts in Mathematics, Vol. 271

Integer Programming is a rigorous graduate-level introduction to optimization problems in which some or all variables are required to take integer values. Rather than treating integer programming simply as a collection of computational techniques, Conforti, Cornuéjols, and Zambelli emphasize the mathematical structures underlying modern algorithms. The book begins with basic formulations and modeling, introducing fundamental methods such as branch-and-bound and cutting planes, before developing the geometry of linear inequalities and polyhedra. This geometric viewpoint is central: integer optimization problems are studied through convex hulls, valid inequalities, and polyhedral descriptions that explain why modern algorithms work. 

The later chapters move into considerably deeper territory, including perfect formulations, Gomory and split inequalities, intersection cuts, corner polyhedra, structured valid inequalities, reformulations and relaxations, enumeration methods, and semidefinite bounds. The authors balance formal theory with examples and exercises, while each chapter points readers toward further literature and specialized topics. This makes the book useful not only as a textbook but also as a bridge toward research in integer and combinatorial optimization. A major strength is the connection it establishes between abstract mathematical ideas—especially polyhedral geometry—and the techniques employed by practical optimization solvers. 

The book is best suited to advanced undergraduate, graduate, or research-level readers with a solid background in linear algebra, discrete mathematics, and preferably linear programming. It is not primarily a beginner's "how to use an optimization package" manual; its goal is to explain the mathematics behind integer-programming methodology. For mathematically oriented readers interested in operations research, combinatorial optimization, algorithms, or discrete mathematics, it provides a particularly substantial introduction to the field.

Key takeaways

• Integer programming combines discrete mathematics, geometry, and algorithms: the polyhedral viewpoint provides much of the theoretical foundation.
  
• Cutting planes and branch-and-bound are fundamental: the book develops the mathematical reasoning behind techniques that underpin modern integer-programming solvers. 
  
• The scope goes well beyond introductory optimization, reaching Gomory cuts, corner polyhedra, reformulations, enumeration, and semidefinite relaxations.
  
• Best for mathematically mature readers: it is especially valuable as a graduate textbook and as preparation for research in integer and combinatorial optimization.
  

Springer — Integer Programming

Goodreads — Integer Programming]]> Integer Programming
Authors: Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli
Publication date: 2014
Publisher: Springer International Publishing
Series:Graduate Texts in Mathematics, Vol. 271

Integer Programming is a rigorous graduate-level introduction to optimization problems in which some or all variables are required to take integer values. Rather than treating integer programming simply as a collection of computational techniques, Conforti, Cornuéjols, and Zambelli emphasize the mathematical structures underlying modern algorithms. The book begins with basic formulations and modeling, introducing fundamental methods such as branch-and-bound and cutting planes, before developing the geometry of linear inequalities and polyhedra. This geometric viewpoint is central: integer optimization problems are studied through convex hulls, valid inequalities, and polyhedral descriptions that explain why modern algorithms work. 

The later chapters move into considerably deeper territory, including perfect formulations, Gomory and split inequalities, intersection cuts, corner polyhedra, structured valid inequalities, reformulations and relaxations, enumeration methods, and semidefinite bounds. The authors balance formal theory with examples and exercises, while each chapter points readers toward further literature and specialized topics. This makes the book useful not only as a textbook but also as a bridge toward research in integer and combinatorial optimization. A major strength is the connection it establishes between abstract mathematical ideas—especially polyhedral geometry—and the techniques employed by practical optimization solvers. 

The book is best suited to advanced undergraduate, graduate, or research-level readers with a solid background in linear algebra, discrete mathematics, and preferably linear programming. It is not primarily a beginner's "how to use an optimization package" manual; its goal is to explain the mathematics behind integer-programming methodology. For mathematically oriented readers interested in operations research, combinatorial optimization, algorithms, or discrete mathematics, it provides a particularly substantial introduction to the field.

Key takeaways

• Integer programming combines discrete mathematics, geometry, and algorithms: the polyhedral viewpoint provides much of the theoretical foundation.
  
• Cutting planes and branch-and-bound are fundamental: the book develops the mathematical reasoning behind techniques that underpin modern integer-programming solvers. 
  
• The scope goes well beyond introductory optimization, reaching Gomory cuts, corner polyhedra, reformulations, enumeration, and semidefinite relaxations.
  
• Best for mathematically mature readers: it is especially valuable as a graduate textbook and as preparation for research in integer and combinatorial optimization.
  

Springer — Integer Programming

Goodreads — Integer Programming]]>